There is a lot of the enthusiastic student about Mary Katrantzou. There she sits on top of her desk by an open window, hair loose, chunky earrings swinging, cigarette and lighter in hand. She laughs a lot - throws her head back and really laughs - and talks 10 to the dozen; so much so that it takes 20 minutes for her actually to light the cigarette and start smoking it.

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But there's nothing rookie about the set-up behind her: two floors of smart studio, giant gleaming windows and exposed brickwork everywhere, the buzz of hard work emanating from the largely female team, who, according to their boss, are 'problem-solving, exploring, finding a way to get beading on to trousers for production'.

Katrantzou, 29, loves a problem. She talks with earnest glee about 'what a nightmare' it was last season trying to engineer a print on to 40 metres of chiffon in 'godet triangles'. And you can tell she's rather pleased that she 'nearly killed' the Parisian embroidery workshop Lesage, when she sent them a stack of yellow bendy rubber pencils to render on to one of her stand-out autumn 2012 show dresses. 'But I think they enjoyed it,' she adds cheerfully.

'Eye-popping', 'mind-blowing', 'dazzling' are some of the words used to describe this Athenian's womenswear designs. Since 2008, when she graduated from the MA fashion course at Central Saint Martins with a distinction, having pioneered her own digital-print technique, she has earned a reputation as something of a print magician, conjuring hyper-real optical patterns from the most unlikely subject matter - perfume bottles, mantelpieces, spoons, teacups - and engineering them on to bold, structural shapes, most famously her spring/summer 2011 lampshade-shaped skirts.

Mary Katrantzou's 'lampshade' skirt Photo: CATWALKING.COM

For autumn/winter 2012 she took images of everyday objects (bathtubs, hedges, lawns, forks) or made 3-D representations of them (the aforementioned pencils, but also typewriters in the form of breastplates) and manipulated them sometimes beyond recognition (so that from a distance the pencils looked like a tribal embellishment). The objects inspired new shapes and silhouettes that echoed armoury, Elizabethan costume and something utterly of the future. 'It's a slightly tongue-in-cheek way of looking at print,' says Katrantzou, who is a fan of the Surrealists. 'Although you should still be able to look at it from afar and just see a beautiful dress.'

As befits a former student of architecture, her product is a triumph of exquisite artistry and deadly logic. There is a steeliness, not to her manner - she is charm personified - but to her ambition and drive, to her expectations of herself. Her daily schedule is, frankly, terrifying. Back-to-back meetings start at 12 and end early evening, after which she goes home to eat with her boyfriend, perhaps watch a film. But that's just the preamble. 'At about midnight when he goes to bed I'll start responding to emails. [She doesn't have a PA.] I usually have about 150 so that takes a couple of hours. And then I design.' And then she designs? 'From about 1am. It depends how heavy the emails are. If there's a contract in there or an interview I'm doomed. Usually I go to bed about five.'

Sweet Lord. If you were under the impression that building a fashion brand was about colouring in handbags while wearing three-legged trousers, 24 hours with Katrantzou would put you right. She hasn't had a weekend off in four years. But that is why she is selling £30,000 dresses straight off the catwalk and we're not.

OK, so 30 grand is the top price for a hand-crafted showpiece. Her more commercial, simple silk pieces without the embroidery sell from £500 upwards. But, yes, real people do buy those amazing pieces. 'The same women will buy from us at that level every season,' says Katrantzou. 'They're the kind of women who buy couture. What we do isn't quite as bespoke as that but these pieces are hand-finished; you can't put them through a machine. And also for those special clients we know their measurements and it will be fitted to them, so I guess that is couture. It's just more unique in its look than the traditional ballgown. It's more the constructed mini!'

She has been surprised to meet some of her customers. 'They've told me that formerly they never wore colour, usually only black, and yet they've bought our dresses season after season. They buy them for the design. They like the illusion it creates for their body,' she says. 'For me it's not just putting our prints on things; it's about designing the form as well. Because I was trained in architecture it has allowed me to think about balance and symmetry on the body. You work with a bodice in the way you would with any three-dimensional form.'

In fact, before she turned up at Central Saint Martins, Katrantzou had very little interest in fashion. The daughter of a businessman and an interior designer, she grew up in Athens surrounded by interiors magazines and books on architecture. 'I was always tearing up sheets and doing collages so I was artistic in that way.' Her parents were keen for her to get the highest level of education available and insisted she went to university rather than art school, although Saint Martins was always her 'dream'. She ended up in America at the prestigious Rhode Island School of Design studying interior architecture, partly, she says, because she'd heard it was the most difficult place to get into and she's always liked a challenge.

But then, unexpectedly, Cupid challenged her. She met Marios Politis, a fellow Greek, while back at home on holiday. A lecturer in neurology, he was establishing a career in London and persuaded her to come with him. 'I was very, very resentful at the beginning,' she says with good humour. 'I hated London. I thought, "He's destroyed my career!" All my friends were saying, "How can you allow this boy to take you from there to all that?" And then my dad was very unhappy, feeling, "Oh, the child is leaving her education for love." But I really liked him. And very quickly I came to love London and my course and how independent I was there. But even then I never thought fashion. I just liked my boyfriend.'

Fashion came gradually. She did a BA in textiles at Saint Martins - 'I saw it as surface design' - but as she watched her friends creating garments instead of cushions she felt as if she was missing out on some fun. She signed up for an MA in fashion, and her degree show, a collection of padded wool dresses printed in a design of oversized jewellery, attracted attention. In 2008 she produced a small collection of simple shifts and gathered orders. In February 2009, with sponsorship from the Topshop New Generation scheme, she debuted at London Fashion Week, with a collection that placed prints of perfume bottles on to more developed dress shapes.

But it was her spring/summer 2011 collection that really stunned the London audience - not only because of the dazzling depth of her interiors-themed prints and the silhouettes inspired by lampshades and fluttering curtains, but because something so artistic was also entirely wearable. Katrantzou's label is now one of Net-a-Porter's biggest sellers. She has collaborated with Topshop on three sell-out collections, and with Longchamp on a range of bags. Not bad for someone who used to have zero interest in fashion.

She lives with Politis in a flat devoid of colour and print (similarly she usually wears black). Her boyfriend takes full credit for her success. 'He says, "You'd be an unknown architect by now if it wasn't for me. You wouldn't even have a job."' She laughs uproariously. Luckily, he shares her workaholic tendencies. 'He's very busy, very ambitious. He does his own research and papers, so even when I want to take a break he will say, "That's OK for you to say now. Let me ask you in September [the month of the catwalk shows] if you want to be taking a break."' They go out rarely. 'Maybe once a month. We always say that we don't have enough friends and we don't go out enough, but you have to compromise somewhere. If you're building a young company and it's going as fast as this is going and you want to have a really strong relationship then social life gets put to one side.'

Katrantzou is devastated about the situation in Greece. 'The saddest thing is that a lot of my friends, who wanted to do so many things, now feel as if there's a cap on everything. For those aged 16 or 17, creatively, culturally, they will come through the turmoil and get something great out of it. But for the people beyond that, at the time when they want to further their career or start a family, it is really difficult. Anyone who can do so is leaving Athens because they just can't see the light.' She says she finds it hard to be there. 'Now after a week I don't know if I can do it any longer. You go out for drinks with friends and it is the only point of discussion. Then there's silence.'

For the first time she is taking a summer holiday elsewhere - and, for once, won't be managing production of the collection from her phone. 'I'd be in Paros texting beneath the table and my boyfriend would say, "Mary! I see you!"' They're going to Cuba and Miami. 'I only have six days off, so how much can you fit in?' she asks, shrugging.

Is she joking? Six whole days on Mary Katrantzou time? Cuba doesn't stand a chance.